Arguments

n.or.n1

numeric vector of sample sizes. When sample.type="one.sample",
n.or.n1 denotes n, the number of observations in the single sample. When sample.type="two.sample", n.or.n1 denotes n_1, the number
of observations from group 1.
Missing (NA), undefined (NaN), and infinite (Inf, -Inf)
values are not allowed.

n2

numeric vector of sample sizes for group 2. The default value is the value of
n.or.n1. This argument is ignored when sample.type="one.sample".
Missing (NA), undefined (NaN), and infinite (Inf, -Inf)
values are not allowed.

delta.over.sigma

numeric vector specifying the ratio of the true difference (δ) to the
population standard deviation (σ). This is also called the
“scaled difference”.

power

numeric vector of numbers between 0 and 1 indicating the power
associated with the hypothesis test. The default value is power=0.95.

sample.type

character string indicating whether to compute power based on a one-sample or
two-sample hypothesis test. When sample.type="one.sample", the computed
power is based on a hypothesis test for a single mean. When sample.type="two.sample", the computed power is based on a hypothesis test
for the difference between two means. The default value is sample.type="one.sample" unless the argument n2 is supplied.

alternative

character string indicating the kind of alternative hypothesis. The possible values
are "two.sided" (the default), "greater", and "less".

approx

logical scalar indicating whether to compute the power based on an approximation to
the non-central t-distribution. The default value is FALSE.

tol

numeric scalar indicating the tolerance argument to pass to the
uniroot function.
The default value is tol=1e-7.

maxiter

positive integer indicating the maximum number of iterations
argument to pass to the uniroot function. The default value is
maxiter=1000.

Details

Formulas for the power of the t-test for specified values of
the sample size, scaled difference, and Type I error level are given in
the help file for tTestPower. The function tTestAlpha
uses the uniroot search algorithm to determine the
required Type I error level for specified values of the sample size, power,
and scaled difference.

Examples

# Look at how the required Type I error level for the one-sample t-test # decreases with increasing sample size. Set the power to 80% and # the scaled difference to 0.5.seq(5,30,by=5)#[1] 5 10 15 20 25 30
alpha <-tTestAlpha(n.or.n1 =seq(5,30,by=5),power=0.8, delta.over.sigma =0.5)round(alpha,2)#[1] 0.65 0.45 0.29 0.18 0.11 0.07#----------# Repeat the last example, but use the approximation.# Note how the approximation underestimates the power # for the smaller sample sizes.#----------------------------------------------------
alpha <-tTestAlpha(n.or.n1 =seq(5,30,by=5),power=0.8, delta.over.sigma =0.5,approx=TRUE)round(alpha,2)#[1] 0.63 0.46 0.30 0.18 0.11 0.07#----------# Look at how the required Type I error level for the two-sample # t-test decreases with increasing scaled difference. Use # a power of 90% and a sample size of 10 in each group.seq(0.5,2,by=0.5)#[1] 0.5 1.0 1.5 2.0
alpha <-tTestAlpha(10, sample.type ="two.sample",power=0.9, delta.over.sigma =seq(0.5,2,by=0.5))round(alpha,2)#[1] 0.82 0.35 0.06 0.01#----------# Look at how the required Type I error level for the two-sample # t-test increases with increasing values of required power. Use # a sample size of 20 for each group and a scaled difference of # 1.
alpha <-tTestAlpha(20, sample.type ="two.sample", delta.over.sigma =1,power=c(0.8,0.9,0.95))round(alpha,2)#[1] 0.03 0.07 0.14#----------# Clean up#---------rm(alpha)